Algebraic Expansions: Broadening the Scope of Architectural Design through Algebraic Surfaces

  • Günter Barczik
  • Daniel Lordick
  • Oliver Labs
Conference paper

Introduction: An Expanded Architectural Design Vocabulary

We conduct a design research project that radicalizes the relationship between tools and design possibilities: we significantly expand the architectural design vocabulary by employing mathematics and computer science as vehicles for accessing shapes that otherwise would be unthinkable: algebraic surfaces, the zero-sets of certain polynomials.

Algebraic surfaces can exhibit geometric features that cannot - or have so far not - be found in nature: puzzling convolutions in which complex geometry and topology combine with high degrees of tautness, harmony and coherence (Fig.1). Albeit mostly curved, they can contain straight lines and any number of plane curves (Fig.1, 1-3). They also look different from every direction, a quality we propose to call polyoptical from the Greek for an object with many faces. Having been studied in mathematics for the last two centuries they became accessible for designers only recently via advances in computer technology. This means a cambrian explosion of shapes, a whole zoo of new exotic shapes.


Mathematical Object Algebraic Surface Subdivision Surface NURBS Surface Large Vocabulary 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Günter Barczik
    • 1
    • 2
  • Daniel Lordick
    • 3
  • Oliver Labs
    • 4
    • 5
  1. 1.Brandenburg Technical UniversityCottbusGermany
  2. 2.HMGB architectsBerlinGermany
  3. 3.Institute of GeometryUniversity of Technology DresdenGermany
  4. 4.Mathematics and its DidacticsCologne UniversityGermany
  5. 5.Institute for Mathematics and Computer ScienceSaarbrücken UniversityGermany

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